The 2D position of a defect as well as its through-thickness length can be measured by ultrasonic time-of-flight diffraction technique (TOFD). By considering the methods used for detecting and positioning a target in radar, acoustic and sonar systems, an algorithm was developed for 3D positioning of defects in TOFD measurements. In this algorithm, the unknown parameter to be determined is the time difference of arrival (TDOA). While the developed algorithm is sufficiently fast, it suffers from various errors affecting the TDOA. The sensitivity of TDOA to errors is more noticeable when the distance between the receivers and the midplane (a plane with a minimum distance from the receivers) is small. This problem cannot be easily resolved when the receivers are coplanar. In this paper, using a closed form solution, a new algorithm is proposed for solving this problem. In this algorithm, by considering hypothetical locations for receivers, both the target (defect) and the positions of receivers are simultaneously verified. These hypothetical positions are obtained in such a way that their distances from the midplane is within acceptable limits. To validate the algorithm, it is used for determining the position of an artificial defect in a carbon steel block. The results prove that the algorithm is accurate and can be used in case of 3D TOFD measurements in which the receivers are usually coplanar.

Keywords: Wave Source positioning, Ultrasonic Time of Flight diffraction (ToFD), Defect positioning and sizing

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